Mechanics of Materials, 7th Edition
7th Edition
ISBN: 9780073398235
Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David F. Mazurek
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 3.5, Problem 69P
Determine the required thickness of the 50-mm tubular shaft of Concept Application 3.7, if it is to transmit the same power while rotating at a frequency of 30 Hz.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
1. The endurance limit for rotating shaft, if its
ultimate strength Su=1600 Mpa is:
The motor on the left provides a torque of 5500 N•m to the gear shaft shown. The motor runs machines connected to gears B, C and D requiring torques of 3000 N•m, 1500 N•m and 1000 N•m respectively. A, B, C and D are spaced 2000 mm apart and the diameter of the shaft is 75 mm. The shear modulus of the shaft material is 80x109 N/m2.
Determine:
Minimum diameter required (in millimeters) if the shearing stress in the shaft is limited to 100x106 N/m2
Rotation of D with respect to A
Note: Draw the Free Body Diagram, Compute for all of the necessary elements, Include the units/dimensions, use the proper formula and round-off all the answers and final answers to 3 decimal places.
A solid steel shaft, whose Sy= 300 MPa and Su= 400 MPa, is used to transmit 3000 kW at 800 rpm. Determine its diameter.
Chapter 3 Solutions
Mechanics of Materials, 7th Edition
Ch. 3.1 - Determine the torque T that causes a maximum...Ch. 3.1 - For the cylindrical shaft shown, determine the...Ch. 3.1 - (a) Determine the torque T that causes a maximum...Ch. 3.1 - (a) Determine the maximum shearing stress caused...Ch. 3.1 - (a) For the 3-in.-diameter solid cylinder and...Ch. 3.1 - Fig. P3.6 3.6 A torque T=3 kN m is applied to the...Ch. 3.1 - The solid spindle AB is made of a steel with an...Ch. 3.1 - The solid spindle AB has a diameter ds = 1.5 in....Ch. 3.1 - Fig. P3.9 and P3.10 3.10 The shafts of the pulley...Ch. 3.1 - Knowing that each of the shafts AB, BC, and CD...
Ch. 3.1 - Fig. P3.11 and P3.12 3.12 Knowing that an...Ch. 3.1 - Under normal operating conditions, the electric...Ch. 3.1 - In order to reduce the total mass of the assembly...Ch. 3.1 - The allowable shearing stress is 15 ksi in the...Ch. 3.1 - The allowable shearing stress is 15 ksi in the...Ch. 3.1 - The solid shaft shown is formed of a brass for...Ch. 3.1 - Solve Prob. 3.17 assuming that the direction of Tc...Ch. 3.1 - The solid rod AB has a diameter dAB= 60 mm and is...Ch. 3.1 - Fig. P3.19 and P3.20 3.20 The solid rod AB has a...Ch. 3.1 - A torque of magnitude T = 1000 N m is applied at D...Ch. 3.1 - Fig. P3.21 and P3.22 3.22 A torque of magnitude T...Ch. 3.1 - Under normal operating conditions a motor exerts a...Ch. 3.1 - Fig P3.23 and P3.24 3.24 Under normal operating...Ch. 3.1 - Prob. 25PCh. 3.1 - Fig. P3.25 and P3.26 3.26 The two solid shafts are...Ch. 3.1 - For the gear train shown, the diameters of the...Ch. 3.1 - Fig. P3.27 and P3.28 3.28 A torque T = 900 N m is...Ch. 3.1 - Fig. P3.29 3.29 While the exact distribution of...Ch. 3.1 - Fig. P3.30 3.30 (a) For a given allowable shearing...Ch. 3.3 - Determine the largest allowable diameter of a...Ch. 3.3 - The ship at A has just started to drill for oil on...Ch. 3.3 - (a) For the solid steel shaft shown, determine the...Ch. 3.3 - (a) For the aluminum pipe shown (G = 27 GPa),...Ch. 3.3 - The electric motor exerts a 500 N m-torque on the...Ch. 3.3 - The torques shown are exerted on pulleys and B....Ch. 3.3 - The aluminum rod BC (G = 26 GPa) is bonded to the...Ch. 3.3 - The aluminum rod AB (G = 27 GPa) is bonded to the...Ch. 3.3 - The solid spindle AB has a diameter ds = 1.75 in....Ch. 3.3 - Fig. p3.39 and p3.40 3.40 The solid spindle AB has...Ch. 3.3 - Two shafts, each of 78in. diameter, are connected...Ch. 3.3 - Two solid steel shafts each of 30-mm diameter, are...Ch. 3.3 - A coder F, used to record in digital form the...Ch. 3.3 - Fig. p3.43 3.44 For the gear train described in...Ch. 3.3 - The design specifications of a 1.2-m-long solid...Ch. 3.3 - 3.46 and 3.47 The solid cylindrical rod BC of...Ch. 3.3 - 3.46 and 3.47 The solid cylindrical rod BC of...Ch. 3.3 - The design of the gear-and-shaft system shown...Ch. 3.3 - The electric motor exerts a torque of 900 Nm on...Ch. 3.3 - A hole is punched at A in a plastic sheet by...Ch. 3.3 - The solid cylinders AB and BC are bonded together...Ch. 3.3 - Solve Prob. 3.51, assuming that cylinder AB is...Ch. 3.3 - The composite shaft shown consists of a...Ch. 3.3 - Fig. p3.53 and p3.54 3.54 The composite shaft...Ch. 3.3 - Two solid steel shafts (G = 77.2 GPa) are...Ch. 3.3 - Solve Prob. 3.55, assuming that the shaft AB is...Ch. 3.3 - 3.57 and 3.58 Two solid steel shafts are fitted...Ch. 3.3 - 3.57 and 3.58 Two solid steel shafts are fitted...Ch. 3.3 - The steel jacket CD has been attached to the...Ch. 3.3 - A torque T is applied as shown to a solid tapered...Ch. 3.3 - Prob. 61PCh. 3.3 - A solid shaft and a hollow shaft are made of the...Ch. 3.3 - An annular plate of thickness t and modulus G is...Ch. 3.5 - Determine the maximum shearing stress in a solid...Ch. 3.5 - Determine the maximum shearing stress in a solid...Ch. 3.5 - Using an allowable shearing stress of 4.5 ksi,...Ch. 3.5 - Using an allowable shearing stress of 50 MPa,...Ch. 3.5 - While a steel shaft of the cross section shown...Ch. 3.5 - Determine the required thickness of the 50-mm...Ch. 3.5 - A steel drive shaft is 6 ft long and its outer and...Ch. 3.5 - The hollow steel shaft shown (G = 77.2 GPa, all =...Ch. 3.5 - A steel pipe of 3.5-in. outer diameter is to be...Ch. 3.5 - 3.73 The design of a machine element calls for a...Ch. 3.5 - Three shafts and four gears are used to form a...Ch. 3.5 - Three shafts and four gears are used to form a...Ch. 3.5 - The two solid shafts and gears shown are used to...Ch. 3.5 - Fig. P3.76 and P3.77 3.77 The two solid shafts and...Ch. 3.5 - The shaft-disk-belt arrangement shown is used to...Ch. 3.5 - A 5-ft-long solid steel shaft of 0.875-in....Ch. 3.5 - A 2.5-m-long steel shaft of 30-mm diameter rotates...Ch. 3.5 - The design specifications of a 1.2-m-long solid...Ch. 3.5 - A 1.5-m-long tubular steel shaft (G = 77.2 GPa) of...Ch. 3.5 - Fig. P3.82 and P3.83 3.83 A 1.5-m-long tubular...Ch. 3.5 - The stepped shaft shown must transmit 40 kW at a...Ch. 3.5 - The stepped shaft shown rotates at 450 rpm....Ch. 3.5 - Knowing that the stepped shaft shown transmits a...Ch. 3.5 - The stepped shaft shown must rotate at a frequency...Ch. 3.5 - Fig. P3.87 and P3.88 3.88 The stepped shaft shown...Ch. 3.5 - A torque of magnitude T = 200 lbin. is applied to...Ch. 3.5 - Fig. P3.89, P3.90 and P3.91 3.90 In the stepped...Ch. 3.5 - In the stepped shaft shown, which has a full...Ch. 3.8 - The solid circular shaft shown is made of a steel...Ch. 3.8 - Prob. 93PCh. 3.8 - Prob. 94PCh. 3.8 - Prob. 95PCh. 3.8 - Fig. P3.95 and P3.96 3.96 The solid shaft shown is...Ch. 3.8 - It is observed that a straightened paper clip can...Ch. 3.8 - The solid shaft shown is made of a mild steel that...Ch. 3.8 - Prob. 99PCh. 3.8 - Prob. 100PCh. 3.8 - Prob. 101PCh. 3.8 - Prob. 102PCh. 3.8 - Prob. 103PCh. 3.8 - Prob. 104PCh. 3.8 - A solid circular rod is made of a material that is...Ch. 3.8 - Prob. 106PCh. 3.8 - Prob. 107PCh. 3.8 - Prob. 108PCh. 3.8 - Prob. 109PCh. 3.8 - Prob. 110PCh. 3.8 - Prob. 111PCh. 3.8 - A 50-mm diameter cylinder is made of a brass for...Ch. 3.8 - Prob. 113PCh. 3.8 - The solid circular drill rod AB is made of a steel...Ch. 3.8 - Prob. 115PCh. 3.8 - Prob. 116PCh. 3.8 - After the solid shaft of Prob. 3.116 has been...Ch. 3.8 - The hollow shaft shown is made of a steel that is...Ch. 3.8 - Prob. 119PCh. 3.8 - Prob. 120PCh. 3.10 - Determine the smallest allowable square cross...Ch. 3.10 - Prob. 122PCh. 3.10 - Using all = 70 MPa and G = 27 GPa, determine for...Ch. 3.10 - Prob. 124PCh. 3.10 - Determine the largest torque T that can be applied...Ch. 3.10 - Each of the two brass bars shown is subjected to a...Ch. 3.10 - Prob. 127PCh. 3.10 - Prob. 128PCh. 3.10 - Prob. 129PCh. 3.10 - Shafts A and B are made of the same material and...Ch. 3.10 - Prob. 131PCh. 3.10 - Shafts A and B are made of the same material and...Ch. 3.10 - Prob. 133PCh. 3.10 - Prob. 134PCh. 3.10 - Prob. 135PCh. 3.10 - A 36-kipin. torque is applied to a 10-ft-long...Ch. 3.10 - A 4-m-long steel member has a W310 60 cross...Ch. 3.10 - Prob. 138PCh. 3.10 - A 5-kipft torque is applied to a hollow aluminum...Ch. 3.10 - A torque T = 750 kNm is applied to the hollow...Ch. 3.10 - A 750-Nm torque is applied to a hollow shaft...Ch. 3.10 - 3.142 and 3.143 A hollow member having the cross...Ch. 3.10 - A hollow member having the cross section shown is...Ch. 3.10 - A 90-Nm torque is applied to a hollow shaft having...Ch. 3.10 - 3.145 and 3.146 A hollow member having the cross...Ch. 3.10 - 3.145 and 3.146 A hollow member having the cross...Ch. 3.10 - A cooling tube having the cross section shown is...Ch. 3.10 - A hollow cylindrical shaft was designed to have a...Ch. 3.10 - Equal torques are applied to thin-walled tubes of...Ch. 3.10 - A hollow cylindrical shaft of length L, mean...Ch. 3 - A steel pipe of 12-in. outer diameter is...Ch. 3 - A torque of magnitude T = 120 Nm is applied to...Ch. 3 - Fig. P3.152 3.153 Two solid shafts are connected...Ch. 3 - Prob. 154RPCh. 3 - Prob. 155RPCh. 3 - A torque of magnitude T = 4 kNm is applied at end...Ch. 3 - Ends A and D of the two solid steel shafts AB and...Ch. 3 - As the hollow steel shaft shown rotates at 180...Ch. 3 - Prob. 159RPCh. 3 - Prob. 160RPCh. 3 - Prob. 161RPCh. 3 - The shaft AB is made of a material that is...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- Determine the diameter of a solid steel shaft that will transfer 30 MW at 1500 RPM with a 1 degree twist angle for every 20 diameters of length. G=80GN/m2. Give me the solution of this please. Ans. D = 3.03 marrow_forwardQuestion 1 (a) A circular shaft used for transmission is 510mm in length and 50mm in external diameter. It is bored to a diameter of 25mm over part of its length and for the remaining length bored to 38mm diameter. Determine the maximum power that can be transmitted if the shaft is rotating at a speed of 210 rev/min and the shear stress is not to exceed 70MN/m?. (b) If the angle of twist for the section with a 25mm bore is equal to that for the section with a 38mm bore determine the lengths of each section. (c) Answer True or False to the following questions - no explanation required. i. A stepper motor uses an outer and inner electromagnet to control the motion. ii. Ferrous materials do not show a fatigue limit. iii. Failure due to fatigue is not a common occurance and is limited to specific stress conditions. iv. For stress concentration a crack that is parallel to the load is more serious than one that is parallel to the applied load. v. A rougher surface will protect a material and…arrow_forward10. Aline shaft is to transmit 30 kW at 160 r.p.m. It is driven by a motor placed directly under it by means of a belt running on alm diameter pulley keyed to the end of the shaft. The tension in the tight side of the belt is 2.5 times that in the slack side and the centre of the pulley over-hangs 150 mm beyond the centre line of the end bearing. Determine the diameter of the shaft, if the allowable shear stress is 56 MPa and the pulley weighs 1600 N. [Ans. 60 mmarrow_forward
- The composite shaft shown consists of two steel pipes that are connected at flange B and securely attached to rigid walls at A and C. Steel pipe (1) has an outside diameter of 164 mm and a wall thickness of 7 mm. Steel pipe (2) has an outside diameter of 114 mm and a wall thickness of 6 mm. Both pipes are 3-m long and have a shear modulus of 80 GPa. If a concentrated torque of 20 kN-m is applied to flange 8, determine the torque in pipe (1). ... 3 m 3 m 20 kN-m (1) (2) B A 10.98 kN-m в) 15.63 kN-m 9.40 kN-m 14.85 kN-marrow_forwardThe composite shaft shown consists of two steel pipes that are connected at flange B and securely attached to rigid walls at A and C. Steel pipe (1) has an outside diameter of 164 mm and a wall thickness of 7 mm. Steel pipe (2) has an outside diameter of 114 mm and a wall thickness of 6 mm. Both pipes are 3-m long and have a shear modulus of 80 GPa. If a concentrated torque of 20 kN-m is applied to flange B, determine the torque in pipe (1).arrow_forwardA compound shaft drives several pulleys, as shown. Segments (1) and (2) of the compound shaft are hollow aluminum (G = 4000 ksi) shafts that have a polar moment of inertia of J = 2.835 in4. Segments (3) and (4) are solid steel (G = 12000 ksi) shafts that have polar moment inertia of J = 1.024 in4. The bearings shown allow the shaft to turn freely. Assume TB = 980 lb.ft TD= 525 lb.ft TE = 130lb.ft L1 =74in L2 =29in L3 =34in L4 =35in. Calculate the rotation angle (including the correct sign) of pulley E with respect to point A.arrow_forward
- The axis ABCD receives a torque of 500Nm from the motor and transmits movement to other devices, by means of belts and pulleys connected at B and C. If it is known that the torques exerted on pulleys B and C are as shown In the figure, determine the minimum radius the shaft must have. You should consider that at point D of the motor there is a bearing that acts as a support for the shaft as at point A. The material of the shaft and its allowable shear stress are indicated in the drawing.Determine:to. Free-Body diagram.b. Shear force diagrams.c. Bending moment diagrams.d. Identification of the critical point of the axis.e. Calculation of the axis radius. tperm=80MPaarrow_forwardIn the gear system shown, the motor applies a torque of 290 N-m to the gear at A. Shaft (1) is a solid 35-mm-diameter shaft, and shaft (2) is a solid 50-mm-diameter shaft. The bearings shown allow free rotation of the shafts. Determine the torque TE provided by the gear system at gear E. B 72 teeth 30 teeth TE (2) E 24 teeth 60 teetharrow_forward3. Two shafts whose centers are 1 m apart are connected by a V-belt drive. The driving pulley is supplied with 100 kW and has an effective diameter of 300 mm. It runs at 1000 r.p.m. while the driven pulley runs at 375 r.p.m. The angle of groove on the pulleys is 40°. The permissible tension in 400 mm2 cross-sectional area belt is 2.1 MPa. The density of the belt is 1100 kg/m3. The coefficient of friction between the belt and pulley is 0.28. Estimate the number of belts required. Answer. 10arrow_forward
- Problem 2: Consider the two gears mounted on the shaft, as shown. Distances are L1 = 100 mm, L2 = 250 mm, and L3 = 175 mm. Diameter of shaft AB is 15 mm, diameter of shaft BC is 20 mm, and diameter of shaft CD is 17.5 mm. Young's modulus for each portion is 200 GPa. Determine the displacement of point D with reference to point A. Also, determine the displacement of point A relative to C. b. Determine the axial strain at any point in shaft segments AB, BC and CD, respectively. If Poisson's ratio for the material of the shafts is v = 0.2, determine the lateral strain in each of the shaft segments. Based on your answers to part (a), do the gears move towards each other, or do they separate from each other? Note that in real gearboxes, movement of gears towards or away from each other is prevented by using thrust bearings. 10 kN 4 kN 5 kN 7 kN 4 kN NY 0I 17.arrow_forwardThe compound shaft shown is composed of a solid circular aluminum (G = 4000 ksi) shaft AB and BC, a hollow brass (6000 ksi) shaft CD and a thin-walled steel (G=12000 ksi) tube DE. The whole assembly is fixed at E. CD and DE are connected together using the flanged-bolt coupling shown with steel (G= 12000 ksi) bolts four of which have a 1-inch diameter and six of which have a 0.5-inch diameter. Meanwhile, BC and CD is attached using a flanged-bolt coupling consisting of eight steel (G= 12000 ksi) 0.75-mm diameter bolts forming a bolt circle with diameter of 6 inches. The 30 kipft torque acts on the right flange at D, the torque T acts on the right flange at C, and the 10 kipft torque acts on the rigid bar at B that connects AB and BC. Determine the following: a. Maximum shear stress in BC (ksi) b. Minimum shear stress in CD (ksi) c. Maximum shear stress in DE (ksi) d. Maximum shear stress in the bolts at C (ksi) e. Maximum shear stress in the bolts at D (ksi) f. Angle of rotation at end…arrow_forwardTwo identical ball bearings Pand Qare operating at loads 30 kN and 45 kN respectively The ratio of the life of bearing P to the life of bearing Q is....arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Understanding Torsion; Author: The Efficient Engineer;https://www.youtube.com/watch?v=1YTKedLQOa0;License: Standard YouTube License, CC-BY